In log shipping the log is backed up. The log includes both open and close transactions. Each time that the log is being restored the server applies all the transactions (open and close transactions). Since in log shipping the restore is done with norecovery option or with standby option, the server knows that it will have another log with the continuation of the open transaction. As long as you are using one of those options (and with log shipping you should use it all the time), you'll restore the open transaction. If something goes wrong with your source server/database and you want to use the target database from you log shipping, you'll have to bring it online by running the last restore with recovery option. At that point, since there will be no other restore that might close the open transactions, the server will rollback all the open transactions.

Adi